Elliptic curve search results

Results (6 matches)

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
28224.2-h2	28224.2-h	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	28224.2	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{22} \cdot 3^{10} \cdot 7^{13} \)	$2.00611$	$(-2a+1), (-3a+1), (3a-2), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{4} \cdot 3 \)	$1$	$0.161471043$	2.237408416	\( \frac{2501041836936508}{124571584809} a - \frac{3039469496037370}{124571584809} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2663 a + 3493\) , \( 28801 a + 52668\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2663a+3493\right){x}+28801a+52668$
37632.2-d2	37632.2-d	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	37632.2	\( 2^{8} \cdot 3 \cdot 7^{2} \)	\( 2^{22} \cdot 3^{4} \cdot 7^{13} \)	$2.15570$	$(-2a+1), (-3a+1), (3a-2), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{4} \)	$1$	$0.279676052$	1.291768351	\( \frac{2501041836936508}{124571584809} a - \frac{3039469496037370}{124571584809} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 888 a - 1164\) , \( 14220 a - 11772\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\left(888a-1164\right){x}+14220a-11772$
37632.2-i2	37632.2-i	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	37632.2	\( 2^{8} \cdot 3 \cdot 7^{2} \)	\( 2^{22} \cdot 3^{4} \cdot 7^{13} \)	$2.15570$	$(-2a+1), (-3a+1), (3a-2), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{5} \cdot 3 \)	$0.256090708$	$0.279676052$	3.969718467	\( \frac{2501041836936508}{124571584809} a - \frac{3039469496037370}{124571584809} \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -1164 a + 276\) , \( -14220 a + 11772\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(-1164a+276\right){x}-14220a+11772$
65856.2-e2	65856.2-e	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	65856.2	\( 2^{6} \cdot 3 \cdot 7^{3} \)	\( 2^{22} \cdot 3^{4} \cdot 7^{19} \)	$2.47941$	$(-2a+1), (-3a+1), (3a-2), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	\( 2^{4} \)	$1$	$0.105707611$	1.952970177	\( \frac{2501041836936508}{124571584809} a - \frac{3039469496037370}{124571584809} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -7933 a + 6651\) , \( -59567 a + 275665\bigr] \)	${y}^2={x}^{3}+{x}^{2}+\left(-7933a+6651\right){x}-59567a+275665$
65856.3-c2	65856.3-c	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	65856.3	\( 2^{6} \cdot 3 \cdot 7^{3} \)	\( 2^{22} \cdot 3^{4} \cdot 7^{19} \)	$2.47941$	$(-2a+1), (-3a+1), (3a-2), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$6.947467229$	$0.105707611$	3.392049076	\( \frac{2501041836936508}{124571584809} a - \frac{3039469496037370}{124571584809} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -3611 a + 8486\) , \( 234601 a + 27418\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\left(-3611a+8486\right){x}+234601a+27418$
112896.2-i2	112896.2-i	$4$	$4$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	112896.2	\( 2^{8} \cdot 3^{2} \cdot 7^{2} \)	\( 2^{22} \cdot 3^{10} \cdot 7^{13} \)	$2.83706$	$(-2a+1), (-3a+1), (3a-2), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{5} \)	$1$	$0.161471043$	1.491605611	\( \frac{2501041836936508}{124571584809} a - \frac{3039469496037370}{124571584809} \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2663 a + 3493\) , \( -28801 a - 52668\bigr] \)	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2663a+3493\right){x}-28801a-52668$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.